When congestion occurs in a node due to high
packet arrival rates, the IDS cannot afford to monitor
the all arrival packets and the buffer overflow
happens. So the IDS becomes ineffective and
deteriorated. Hence, it is desirable to assign IDS
node to the network properly so that prevent the
denial of IDS service due to the overflow.
In this paper, we propose a monitoring node
selection algorithm for intrusion detection in
congested sensor network. By using queuing theory,
we prevent congested monitoring situations. In
congested system, our proposed scheme has the
longest network lifetime and the smallest total
battery consumption than other existing schemes. By
preventing congested monitoring tasks, our
algorithm guarantees QoS of monitoring tasks and
reliable sensor networks.
2 ALGORITHM
We propose an IDS node selection scheme based on
two requirements. First, to monitor all nodes in the
network, every node should be in the monitoring
coverage of IDS. Second, to prevent the congestion
of monitored packets, we design the IDS nodes
placement scheme considering congested systems.
For satisfying the first requirement, we apply a set
covering problem (SCP) to the IDS nodes selection
scheme.
The SCP is a classical question in computer
science and complexity theory. The SCP selects a
minimum number of sets that contain all elements
and additionally minimizes the cost of the sets.
Therefore, the SCP guarantees that every element is
covered by at least one server at minimal total cost.
To cover all nodes by minimal IDS, we propose a
formulation using the SCP. The formulation of the
IDS node placement scheme using the SCP is as
follows;
1
1
min
.1
{0,1}
n
jj
j
n
ij j
j
j
cx
taxiN
jN
=
=
≥ ∀ ∈
∈ ∀ ∈
∑
∑
(1)
Formulation (1) is a typical SCP formulation.
Binary variable x
j
is one if node j is IDS node, and
zero otherwise. Like figure 1, binary variable a
ij
is
one if node j is in the transmission range of node i,
and zero otherwise. In the typical SCP, c
j
is the cost
which is needed to select server j. In this problem,
every node has same weight. Therefore, we define c
j
of every node as 1. We define the set N as the set of
all nodes in the network.
Figure 1: Transmission range of a wireless node.
Formulation (1) satisfies the first requirement.
Then, we discuss a constraint considering congested
systems. An implicit assumption in traditional SCP
is that each node in the coverage of a server always
receive satisfied service. However, when a server
suffers from congestion by excessive demand, some
users are not able to receive satisfied service in the
real situation. Especially, if an IDS node suffers
from congestion of monitored packets, intrusion
detection efficiency is reduced and battery
consumption of the IDS is high. In order to
guarantee high detection rate and use efficiently
limited wireless resources, considering congested
systems is important. To prevent congestions, any
packet should not stand in waiting line in the buffer
of IDS nodes for a time longer than a given time-
limit (Marianov, V. and Serra, D., 1998). The
constraint which considers congestion is as follows;
[]P waiting time at IDS node j j
α
≤ ≥ ∀
.
(2)
Constraint (2) makes the total time spent by a
packet at the IDS node shorter than equal to τ with
probability of at least α. The variables τ and α are
predefined time and probability. In order to express
constraint (2) as a numerical formula, we use the
queuing theory (Marianov, V. and Serra, D., 1998).
In this paper, we make an assumption that an packet
arrival rate from node i to j appears according to a
poisson process with intensity f
ij
. Also, we assume
an exponentially distributed monitoring service time,
with an average rate of μ
j
. This is a reasonable
assumption, since IDS systems behave as M/M/1
queuing systems. As we assume a M/M/1 queuing
system, we are able to use the well known results for
a M/M/1 queuing system for each IDS and its
allocated nodes (Marianov, V. and Serra, D., 1998).
Rewriting constraint (2) as a numerical formula, we
get
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